History of solving equations in general

Senior Seminar Guidelines:

Choosing a Topic for the Final Paper, Writing the Final Paper,

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and Not Screwing Up the Presentation

What sort of topic can be chosen for the final paper?

 

Well, you certainly need to choose a topic in mathematics you might actually be interested in

studying, otherwise the final paper will be an absolute nightmare. Your topic should fall within one of the

following two categories:

 

1. Something you’ve already learned about but would like to explore more deeply.

2. Something you’ve read about or heard of that sounded cool but you don’t know much about.

 

In other words, your final paper must either deal with a topic that you have seen before but are

willing to do some more advanced investigations in, or something that you have had little or no

experience with (in which case your investigations might not be so advanced, out of necessity). With this

in mind, your topic can be pretty much anything you want, as long as it comes from within mathematics.

For those of you in mathematics education, you will not be writing a lesson plan, or talking about

technology in pedagogy, but doing actual mathematics. For those of you in statistics, you will not be

writing a program to analyze data, you will be delving into the mathematical content of your subject, and

not simply number crunching.

 

You’ve thought about possible topics for days, which included hours of sobbing and banging your

head against the wall, and still you have absolutely no idea what to do for the stupid paper. Then

what?

 

Then you come to me, and we chat. I will harass you with probing questions until we can find

some bit of math that you actually liked or would like to know more about. Come hell or high water, I

guarantee we will find something that interests you! Of course, to keep your sanity, your chosen subject

should not be too large; it will need to be narrowed down into something manageable (again, I will help).

In any case, it is mandatory that you inform me of your final choice of topic before you begin working on

the paper, so I can judge it as appropriate or not.

 

So you have a topic, great. Now what exactly do you do with it? What is the final paper all about?

 

The final paper is not your typical “go to Wikipedia and look up crap” sort of thing. In this paper, you

will do two things:

 

1. Introduce your topic. I lied: this part will in fact involve accessing the internet in one way or another

to be able to give some historical background for your topic. Tell me how it developed, why anybody

cares about it, who uses it and for what, etc. Also, this is the place where you would introduce any

important terms and/or ideas you will be using in the rest of the paper. The introduction is NOT simply a

list of definitions, rules, equations, and/or theorems that you will need later. The introduction is an

explanation, a discussion, an exposition, where everything is written in paragraph form (as is the entire

paper, of course). While the introduction is important, it is not the most important part of your paper, and

as such it should not be incredibly long. Rather, the truly important part of your paper is:

2. Engage in mathematics within your topic area. You might be wondering what the hell this means… it

means that you must, well, DO some mathematics that you haven’t done before. This is by far the MOST

important part of your paper. So, what does “doing mathematics” actually involve? Among other things,

it can and will involve any and all of the following:

 

a. Solving problems

b. Proving theorems

c. Working with actual research papers in mathematics (for example, filling in the details of hard

proofs, “dumbing down” difficult mathematical concepts for a more general audience, etc.)

d. Working with multiple sources and understanding what to extract to produce a compelling and

organized mathematical narrative (which involves knowing what needs to be defined, and how carefully

explaining all the relevant mathematical tools you’ll be using, etc.)

 

Everything should be perfectly understandable, with a clear, precise, and logical flow of ideas. Your

paper will stand or fall primarily based on the quality of this exposition. The mathematics here should not

be easy, but it doesn’t have to be diabolically hard, either; with my help, you will reach a happy middle.

But let’s be clear, you are not doing original research for this paper!!

 

In any case, it is mandatory that you show me what you want to do before you begin working on anything,

so I can judge it as appropriate or not.

 

What sources do I use in order to figure out what I’m going to do????

1. Books

 

Go to our library’s website, and you will find many ebooks to read. Go and just browse, see what you

find. There are many fabulous authors waiting to enlighten you. (For example, anything written by

Martin Gardner is wonderful, and will get your brain juices flowing.)

 

2. Websites

 

There are lots of cool websites out there chock full of arresting information (for example, like

www.cut-the-knot.org). Of course, there are also crappy websites that don’t know what they’re talking

about. So, if you find an interesting website you’d like to use in some way, show me first, so we can see

if it’s actually decent or not.

 

3. Journals

 

There are many journals that have research articles geared towards undergraduates. My favorites are

Mathematics Magazine and the College Mathematics Journal, but there are plenty of others: Math

Horizons, the Mathematical Gazette, etc. Articles from these journals are accessible from the library’s

website: under “Databases”, find “JSTOR”. You can use JSTOR browse through entire journal issues, or

type in something to search for and see what articles come up.

 

4. My brain

 

I expect you to regularly discuss your topic and paper with me, especially if you’re stuck on something. I

can direct you to an appropriate source, or lend you a useful book, or maybe just email you things to work

on that I think would be good for your paper.

What other boring details should you know about the final paper?

 

There is no set length for the paper. Two pages guarantee you an F, unless you happen to solve

some fabulous research problem (which you are not expected to do, as I said earlier). Fifty pages do not

guarantee you an A (it will guarantee me falling asleep while reading your paper, which isn’t good).

Given your topic and the problems you wish to do in connection with it, you will be able to find a happy

middle (or a sad middle, if you’re depressed). It goes without saying, the paper must be TYPED. If

possible, all equations and diagrams should be done using a computer, not by hand. You must include

references with your paper; in particular, I want to know exactly where you found any information you

used; everything should be well documented in a standard bibliography. Again, I must stress, ALL

sources must be cited appropriately. Plagiarism will result in an automatic F for the paper. Be sure to

write everything in your own words!

 

The presentation part sounds terrifying. What’s going on with that?

 

Your final presentation should last about 15 minutes. The goal of the presentation is to show the

class something interesting from your paper. It can be whatever you want it to be: an amusing activity,

some historical background, whatever cool ideas, pictures, theorems, and/or important points you’d like to

bring out. You don’t have to talk about every stupid little thing you did in the paper; for example, you

could focus on only one part and not mention anything else that you did. What I expect is a light,

informative, entertaining, brief talk (on Blackboard, of course). Here’s some advice on how to handle it:

 

1. Your presentation should focus on some ASPECT of your paper. As such, the paper should be larger

than the presentation. If your paper is exactly the same as your presentation, be ready for a crap grade.

 

2. Your time is limited, so don’t waste too much time writing on the Blackboard whiteboard (ha!). Use

of PowerPoint is strongly suggested.

 

3. Practice your presentation ahead of time! Note how long it takes, and make sure you don’t go over

the time limit. Preparation is important; you’d better know exactly what you’re talking about. Of course,

errors and silly mistakes may creep in anyway, and that’s okay. What’s not okay is to come in

completely brainless and fake your way through the presentation; expect a score of 0 for that.

 

4. Do not go through long, boring proofs and calculations! Focus on presenting interesting things:

strange history, amusing problems, wacky theorems, surprising results, clever proofs and explanations,

etc. are all good. On the other hand, if you really want to talk about a long and complicated proof, give us

an overview of what’s going on, rather than all the gory details.

 

5. There should be a nice flow to your talk, where one idea follows from the next. If it’s so disorganized

that I have no idea why you’re doing what you’re doing, you’ll get a 0. (How pretty your slides are

doesn’t count for much… it’s the content of your presentation that’s important.)

 

6. Do not just SPEAK complicated formulas, as no one will follow what you’re saying. If you’re going

to talk about equations and such, make sure they are written down for all to see.

 

7. DO NOT USE VIDEOS. If you’re going to present a video where you are silent for half of your

presentation, get ready for an F. If there is video footage that aids your presentation, it must be presented

with your own commentary, but should be kept short.

 

8. MAKE YOUR OWN SLIDES. In other words, do not copy anything from any websites or books.

The Powerpoint slides should be your own work, and yours alone. (Same goes for the paper.)

 

9. UNDERSTAND HOW TO WORK BLACKBOARD AS A PRESENTER!!! You’ll have time before

presentations to practice that. I’ll explain everything, but you should definitely attempt to know what

you’re doing with all the tech before it’s go time.

 

10. There’s no need to be nervous. It can be difficult to speak in front of your peers, but everybody will

be supportive of you, even if you screw up, since you’ll all be in the same boat (and if they’re not

supportive, I’ll give them all F’s). So relax!

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